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statistics informed decisions using data

Statistics Informed Decisions Using Data 5th Global Edition Michael Sullivan - Solutions

In a study to determine whether preferences for self are more or less prevalent than preferences for others, researchers first asked individuals to identify the person who is most valuable and likeable to you, or your favorite other. Of the 1519 individuals surveyed, 42 had chosen themselves as
Suppose that E and F are two events and that N(E and F) = 480 and N(E) = 810. What is P(F | E)?
Suppose that E and F are two events and that N(E and F) = 340 and N(E) = 550. What is P(F|E)?
Suppose that E and F are two events and that P(E) = 0.7 and P(F|E) = 0.8. What is P(E and F)?
The probability that a randomly selected individual in a country earns more than \($75\),000 per year is 7.5%. The probability that a randomly selected individual in the country earns more than \($75\),000 per year, given that the individual has earned a bachelor’s degree, is 21.5%. Are the
For the month of June in a certain city, 87% of the days are cloudy. Also in the month of June in the same city, 73% of the days are cloudy and foggy. What is the probability that a randomly selected day in June will be foggy if it is cloudy?
According to a recent study, 8.7% of high school dropouts are 16- to 17-year-olds. In addition, 6.3% of high school dropouts are white 16- to 17-year-olds. What is the probability that a randomly selected dropout is white, given that he or she is 16 to 17 years old?
The data represent the number of driving fatalities for a certain area by age for male and female drivers.(a) What is the probability that a randomly selected driver fatality who was male was 16 to 20 years old?(b) What is the probability that a randomly selected driver fatality who was 16 to 20
Suppose you just received a shipment of nine televisions. Three of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
This past semester, a professor had a small business calculus section. The students in the class were Jinita, William, Al, Allison, Pam, Mike, Neta, and Jim. Suppose the professor randomly selects two people to go to the board to work problems. What is the probability that Pam is the first person
Suppose you just purchased a digital music player and have put 6 tracks on it.After listening to them you decide that you like 2 of the songs.With the random feature on your player, each of the 6 songs is played once in random order. Find the probability that among the first two songs played(a) You
Due to a manufacturing error, eight cans of regular soda were accidentally filled with diet soda and placed into a 24-pack. Suppose that two cans are randomly selected from the 24-pack.(a) Determine the probability that both contain diet soda.(b) Determine the probability that both contain regular
Suppose there is a 24.4% probability that a randomly selected person aged 40 years or older is a smoker. In addition, there is a 13.9% probability that a randomly selected person aged 40 years or older is male, given that he or she smokes. What is the probability that a randomly selected person
Determine the probability that at least 2 people in a room of 13 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions:(a) Compute the probability that 13 people have different birthdays.(b) The complement of “13
Teen Communication The following data represent the number of different communication activities used by a random sample of teenagers in a given week. Complete parts (a) through (d).(a) Are the events “male” and “0 activities” independent?(b) Are the events “female” and “5+
The fixed-price dinner at Mabenka Restaurant provides the following choices:Appetizer: soup or salad Entrée: baked chicken, broiled beef patty, baby beef liver, or roast beef au jus Dessert: ice cream or cheesecake How many different meals can be ordered?Approach Ordering such a meal requires
The International Air Transport Association (IATA) assigns three-letter codes to represent airport locations. For example, the code for Fort Lauderdale International Airport is FLL. How many different airport codes are possible?Approach We are choosing three letters from 26 letters and arranging
Three members from a 14-member committee are to be randomly selected to serve as chair, vice-chair, and secretary. The first person selected is the chair, the second is the vice-chair, and the third is the secretary. How many different committee structures are possible?Approach The task consists of
You have just been hired as a book representative for Pearson Education. On your first day, you must travel to seven schools to introduce yourself. How many different routes are possible?Approach Call the seven schools A, B, C, D, E, F, and G. School A can be visited first, second, third, fourth,
Evaluate:(a) 7P5(b) 5P5By Hand ApproachTechnology ApproachWe will use a TI-84 Plus C graphing calculator in part (a) and Excel in part (b) to evaluate each permutation. The steps for determining permutations using the TI-83/84 Plus graphing calculator, Excel, and StatCrunch can be found in the
In how many ways can horses in a ten-horse race finish first, second, and third?Approach The ten horses are distinct. Once a horse crosses the finish line, that horse will not cross the finish line again, and, in a race, finishing order is important. We have a permutation of ten objects taken three
Roger, Ken, Tom, and Jay are going to play golf. They will randomly select teams of two players each. List all possible team combinations. That is, list all the combinations of the four people Roger, Ken, Tom, and Jay taken two at a time. What is 4C2?Approach List the possible teams. Note that
Evaluate:(a) 4C1(b) 6C4(c) 6C2 By Hand ApproachTechnology Approach We will use a TI-84 Plus C graphing calculator in part (a) and Excel in parts (b) and (c) to evaluate each combination. The steps for determining combinations using the TI-83/84 Plus graphing calculator, Excel, and StatCrunch can
How many different simple random samples of size 4 can be obtained from a population whose size is 20?Approach The 20 individuals in the population are distinct. In addition, the order in which individuals are selected is unimportant. Thus, the number of simple random samples of size 4 from a
A DNA sequence consists of a series of letters representing a DNA strand that spells out the genetic code. There are four possible letters (A, C, G, and T), each representing a specific nucleotide base in the DNA strand (adenine, cytosine, guanine, and thymine, respectively). How many
How many different vertical arrangements are there of 10 flags if 5 are white, 3 are blue, and 2 are red?Approach Because there are nondistinct items and order matters, use the formula for finding the number of permutations with nondistinct items. We seek the number of permutations of n = 10
In the Illinois Lottery, an urn contains balls numbered 1–52. From this urn, six balls are randomly chosen without replacement. For a \($1\) bet, a player chooses two sets of six numbers. To win, all six numbers must match those chosen from the urn. The order in which the balls are picked does
A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The plant’s quality-control manager randomly selects and inspects 5 fasteners. What is the probability that exactly 1 of the inspected fasteners is defective?Approach Find the probability that
Rewrite each logarithmic expression as an equivalent exponential expression.Rewrite each exponential expression as an equivalent logarithmic expression.(a) loga 12 = 5 (b) log10 x = 2(c) 4y = 13 (d) 101.5 = xApproach We use the fact that y = loga x if and only if x = ay.
Write each expression as a sum of logarithms. Express powers as factors.(a) loga x2(b) loga(x4y3)(c) loga(4x3)Approach Use Properties (1) and (2).
Evaluate the following expressions. Round your answers to three decimal places.(a) log 4.5(b) 103.4 Approach Use a calculator to evaluate these expressions.
The data in Table 16 represent the temperature of a pizza removed from an oven measured in 5-minute intervals.(a) Draw a scatter diagram of the data treating time, x, as the explanatory variable.Comment on the shape of the scatter diagram.(b) Determine Y = log y. Draw a scatter diagram treating the
Scott drops a ball from various heights and records the time, x, that it takes for the ball to hit the ground, using a motion detector. He obtains the data displayed in Table 18.(a) Draw a scatter diagram of the data, treating the time, x, as the explanatory variable. Comment on the shape of the
Is the following a probability model? What do we call the outcome “red”? Color Probability Red 0 Green 0.1 Blue 0.1 Brown 0.3 Yellow 0.15 Orange 0.35
Verify that the following is a probability model. If the model represents the colors of M&Ms in a bag of milk chocolate M&Ms, explain what the model implies. Color Probability Red 0 Green 0 Blue 0 Brown 0 Yellow 1 Orange 0
Why is the following not a probability model? Color Probability Red 0.3 Green -0.4 Blue 0.2 Brown 0.4 Yellow 0.2 Orange 0.3
Which of the following numbers could be the probability of an event?0.33, −0.54, 1, 0, 1.16, 0.01
In a certain card game, the probability that a player is dealt a particular hand is 0.48. Explain what this probability means. If you play this card game 100 times, will you be dealt this hand exactly 48 times? Why or why not?
Suppose you toss a coin 100 times and get 54 heads and 46 tails. Based on these results, what is the probability that the next flip results in a head?
According to a certain country’s education department, 43.6% of 3-year-olds are enrolled in day care. What is the probability that a randomly selected 3-year-old is enrolled in day care?
Compute the probability of the event E = {1, 2}.Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event E = “an even number less than 8.”Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Compute the probability of the event E = “an even number.”Let the sample space be S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Suppose the outcomes are equally likely.
Planting Tulips A bag of 100 tulip bulbs purchased from a nursery contains 35 red tulip bulbs, 20 yellow tulip bulbs, and 45 purple tulip bulbs.(a) What is the probability that a randomly selected tulip bulb is red?(b) What is the probability that a randomly selected tulip bulb is purple?(c)
A police officer randomly selected 555 police records of larceny. The accompanying data represent the number of offenses for various types of larceny.(a) Construct a probability model for type of larceny.(b) Are coin-operated-machine larcenies unusual?(c) Are bicycle larcenies unusual? Type of
Dominique, Marco, and John work for a publishing company. The company wants to send two employees to a statistics conference. To be fair, the company decides that the two individuals who get to attend will have their names randomly drawn from a hat.(a) Determine the sample space of the experiment.
A baseball player hit 69 home runs in a season. Of the 69 home runs, 22 went to right field, 23 went to right center field, 10 went to center field, 12 went to left center field, and 2 went to left field.(a) What is the probability that a randomly selected home run was hit to right field?(b) What
(a) Roll a single die 50 times, recording the result of each roll of the die. Use the results to approximate the probability of rolling a three.(b) Roll a single die 100 times, recording the result of each roll of the die. Use the results to approximate the probability of rolling a three.(c)
Determine whether the probabilities below are computed using the classical method, empirical method, or subjective method.(a) The probability of having six girls in a six-child family is 0.015625.(b) On the basis of a survey of 1000 families with six children, the probability of a family having six
In a recent survey, it was found that the median income of families in country A was \($57\),000. What is the probability that a randomly selected family has an income less than \($57\),100?
State the definition of a logarithm.
What is the linear form of y = abx?
Suppose that data are known to be related through the equation y = axb. What variables need to be transformed to use linear least-squares to estimate a and b?
25 = 32 Change each exponential expression to an equivalent expression involving a logarithm.
x5 = 18 Change each exponential expression to an equivalent expression involving a logarithm.
c3 = 21 Change each exponential expression to an equivalent expression involving a logarithm.
7x = 15 Change each exponential expression to an equivalent expression involving a logarithm.
12x = 43 Change each exponential expression to an equivalent expression involving a logarithm.
53 = y Change each exponential expression to an equivalent expression involving a logarithm.
61.5 = y Change each exponential expression to an equivalent expression involving a logarithm.
log3 81 = 4 Change each logarithmic expression to an equivalent expression involving an exponent.
log4 64 = 3 Change each logarithmic expression to an equivalent expression involving an exponent.
loga 14 = 3 Change each logarithmic expression to an equivalent expression involving an exponent.
logb 19 = 4 Change each logarithmic expression to an equivalent expression involving an exponent.
log4 c = 3 Change each logarithmic expression to an equivalent expression involving an exponent.
log5 b = 4 Change each logarithmic expression to an equivalent expression involving an exponent.
log2 5 = k Change each logarithmic expression to an equivalent expression involving an exponent.
log6 24 = w Change each logarithmic expression to an equivalent expression involving an exponent.
log3(uv)Write each expression as a sum of logs. Express powers as factors.
log2(ab)Write each expression as a sum of logs. Express powers as factors.
log5 x4 Write each expression as a sum of logs. Express powers as factors.
log7 y3 Write each expression as a sum of logs. Express powers as factors.
loga(uv2)Write each expression as a sum of logs. Express powers as factors.
loga(x3y)Write each expression as a sum of logs. Express powers as factors.
log(x4y3)Write each expression as a sum of logs. Express powers as factors.
log(x6y2)Write each expression as a sum of logs. Express powers as factors.
log 34Use a calculator to evaluate each expression. Round your answers to three decimal places.
log 18 Use a calculator to evaluate each expression. Round your answers to three decimal places.
log 13.2 Use a calculator to evaluate each expression. Round your answers to three decimal places.
log 34.1 Use a calculator to evaluate each expression. Round your answers to three decimal places.
101.6 Use a calculator to evaluate each expression. Round your answers to three decimal places.
102.3 Use a calculator to evaluate each expression. Round your answers to three decimal places.
100.36 Use a calculator to evaluate each expression. Round your answers to three decimal places.
100.74 Use a calculator to evaluate each expression. Round your answers to three decimal places.
The following data, obtained from the U.S. Census Bureau, represent the population of the United States. An ecologist is interested in finding an equation that describes the population of the United States over time. She is convinced that the population is growing exponentially(a) Draw a scatter
The following data represent the amount of money an investor has in an investment account each year for the last 6 years. The theory of finance states that account values grow exponentially over time.(a) Draw a scatter diagram treating time as the explanatory variable.(b) Determine the logarithm of
David is conducting an experiment to estimate the acceleration of an object due to gravity. He takes a ball, drops it from different heights, and records the time that it takes for the ball to hit the ground using an optic laser connected to a stop watch. He collects the following data:The theory
Cathy is conducting an experiment to measure the relation between a light bulb’s intensity and the distance from the light source. She measures a 100-watt light bulb’s intensity 1 meter from the bulb and at 0.1-meter intervals up to 2 meters from the bulb and obtains the following data.Physics
The period of a pendulum is the time required for one oscillation; the pendulum is usually referred to as simple when the angle made with the vertical is less than 5°. An experiment is conducted in which simple pendulums are constructed with different lengths, and the corresponding periods are
Depreciation The following data represent the asking price, y, and age, x, of a Chevrolet Impala(a) Determine the linear least-squares regression line, treating age as the explanatory variable. Plot the residuals against the explanatory variable, age. Do you believe the relation between age and
Go to the book’s website and download the file 4_5_46. The data represent the percentage of putts made by golfers on the PGA Tour at different distances from the hole. For example, at a distance of 2 feet from the hole, 99.3% of putts are made. Build a model that describes the relation between
The data shown in Table 17 show the finishing times (in minutes) of the men in the 60- to 64- year-old age group in a 5-kilometer race. Determine the five-number summary of the data.Approach The five-number summary requires the minimum data value, Q1, M (the median), Q3, and the maximum data value.
Using statistical software or a graphing calculator, determine the five-number summary of the data presented in Table 17.Approach We will use Minitab to obtain the five-number summary. Table 17 19.95 23.25 23.32 25.55 25.83 26.28 42.47 28.58 28.72 30.18 30.35 30.95 32.13 49.17 33.23 33.53 36.68
Use the results from Example 1 to construct a boxplot of the finishing times of the men in the 60- to 64-year-old age group.Data from Example 1The data shown in Table 17 show the finishing times (in minutes) of the men in the 60- to 64-year-old age group in a 5- kilometer race. Determine the
In the Spacelab Life Sciences 2, led by Paul X. Callahan, 14 male rats were sent to space. The red blood cell mass (in milliliters) of the rats was determined when they returned. A control group of 14 male rats was held under the same conditions (except for space flight) as the space rats, and
A golf pro wants to investigate the relation between the club-head speed of a golf club (measured in miles per hour) and the distance (in yards) that the ball will travel. He realizes other variables besides club-head speed determine the distance a ball will travel (such as club type, ball type,
For the data shown in Table 2, compute the linear correlation coefficient. A scatter diagram of the data is shown in Figure 6. The dashed lines on the scatter diagram represent the mean of x and the mean of y.Formula 1 Figure 6 Table 2 x y 20 20 1 18 18- 3 13 16 3 6 9 9 14- 12- 7 4 10 8- 6- 4 2 0
Use a statistical spreadsheet or a graphing calculator with advanced statistical features to draw a scatter diagram of the data in Table 1. Then determine the linear correlation between club-head speed and distance.Approach We will use Excel to draw the scatter diagram and obtain the linear
Using the results from Example 3, determine whether a linear relation exists between club-head speed and distance.Data from Example 3Use a statistical spreadsheet or a graphing calculator with advanced statistical features to draw a scatter diagram of the data in Table 1. Then determine the linear
Because colas tend to replace healthier beverages and colas contain caffeine and phosphoric acid, researchers Katherine L. Tucker and associates wanted to know whether cola consumption is associated with lower bone mineral density in women. Table 4 lists the typical number of cans of cola consumed

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